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Abstract

We present an optomechanical method to tune phase and group birefringence in parallel silicon strip waveguides. We first calculate the deformation of suspended, parallel strip waveguides due to optical forces. We optimize the frequency and polarization of the pump light to obtain a 9nm deformation for an optical power of 20mW. Widely tunable phase and group birefringence can be achieved by varying the pump power, with maximum values of 0.026 and 0.13, respectively. The giant phase birefringence allows linear to circular polarization conversion within 30µm for a pump power of 67mW. The group birefringence gives a tunable differential group delay of 6fs between orthogonal polarizations. We also evaluate the tuning performance of waveguides with different cross sections.

M. I. T. Photonic Bands, (MPB) is a free software package for the solution of the electromagnetic eigenmodes of periodic structures. MPB has been developed at MIT, http://ab-initio.mit.edu/wiki/index.php/MPB .

M. I. T. Photonic Bands, (MPB) is a free software package for the solution of the electromagnetic eigenmodes of periodic structures. MPB has been developed at MIT, http://ab-initio.mit.edu/wiki/index.php/MPB .

Figures (7)

(a) Two coupled Si waveguides, each with cross section w×h separated by a distance d, rest on a SiO2 substrate with a free-standing section of length L. (b) Dispersion relation for the lowest-frequency TE mode (solid lines) and TM mode (dashed lines) of the coupled waveguides for several separations. Insets respectively show the Ey field distribution of the TE mode and the Ez field distribution of the TM mode with d=0.2a at frequency ωa/2πc=0.18 (darker shades correspond to larger magnitudes of the electric field at a snapshot in time). The yellow region shows the light cone.

(a) Normalized force per unit area for the lowest-frequency TE (red) and TM (black) modes as a function of pump light frequency, at fixed separation d=0.35a. (b) Force per unit area as a function of separation (red triangles), at optimized frequency ωpa/2π c=a/λp=0.165. The right and top axes are in physical units with incident power P=20 mW, w=h=a=263.5nm, and L=30 µm. The blue solid line is the second-order polynomial fit of the force per unit area.

Displacement of the suspended section of each waveguide as a function of position along the waveguide. The cross-sectional dimension is w=h=a=263.5nm, the initial waveguide separation is d=0.35a ≈92.2nm, the pump frequency is ωpa/2πc=a/λp=0.165, the incident power is P=20 mW, and the suspended length is L=30 µm. Note that the x and y axes differ in scale.

(a) Phase birefringence Δnp as a function of signal frequency in the coupled waveguides with varying separations. The arrow shows that at a frequency ωsa/2πc=0.17, the absolute value of Δnp increases as the waveguide separation d decreases. (b) Phase birefringence Δnp as a function of position along the waveguides. The initial separation is d=0.35a≈92.2nm. The attractive force is induced by CW pump light at frequency ωpa/2πc=a/λp=0.165 and power P=20mW. The difference between the maximum and the minimum of │Δnp│ is 0.026.

Tuning the relative phase shift by increasing CW pump power from 20mW to 70mW (black squares). The waveguide length is 23.05µm. The red line is a 2nd –order polynomial fit of the phase shift. A power of approximately 67mW yields a 0.5π phase difference.

Phase birefringence Δnp as a function of signal frequency in the two-waveguide system with varying separations. (a) The cross section of each waveguide is a×2a. The arrow shows that Δnp decreases with decreasing separation. (b) The cross section of each waveguide is a×0.5a. The absolute value of Δnp increases with decreasing separation.

(a) Group birefringence Δng as a function of signal frequency, in the coupled waveguides with varying separations. The arrow shows that as the waveguide separation d increases, the group birefringence Δng increases fastest at a frequency ωsa/2πc=0.17. (b) Group birefringence Δng as a function of position along the waveguides. The waveguides are deformed by an attractive force induced by a CW pump at frequency ωpa/2πc=a/λp=0.165, with a power P=20mW. The difference between the maximum and the minimum of Δng is 0.13.